Question

college prep in the diagram, m∠agc = 38°, m∠cgd = 71°, and m∠fgc = 147°. which of the following statements are true? select all that apply. m∠agb = 19° m∠dgf = 142° m∠agf = 128° ∠bgd is a right angle

Explanation:

Step1: Analyze angle - addition relationships

We know that angles around a point sum to 360°. Also, we can use the given angle measures to find other angles by addition and subtraction.

Step2: Check \(m\angle AGB = 19^{\circ}\)

There is no information given to directly calculate \(\angle AGB\) from the provided \(m\angle AGC = 38^{\circ}\), \(m\angle CGD=71^{\circ}\), and \(m\angle FGC = 147^{\circ}\), so we cannot confirm this.

Step3: Calculate \(m\angle DGF\)

We know that \(m\angle FGC + m\angle CGD+m\angle DGF=180^{\circ}\) (since they form a straight - line). Substituting \(m\angle FGC = 147^{\circ}\) and \(m\angle CGD = 71^{\circ}\), we get \(m\angle DGF=180-(147 + 71)=180 - 218\) which is incorrect. Let's consider the correct relationship: \(m\angle FGC=147^{\circ}\) and \(m\angle CGD = 71^{\circ}\), and since \(\angle FGD\) and \(\angle FGC+\angle CGD\) are supplementary. \(m\angle DGF=180-(147 + 71)\) is wrong. In fact, \(m\angle DGF=180 - 71=109^{\circ}\) (assuming \(\angle FGC\) and \(\angle CGD\) are part of the angle - composition related to \(\angle DGF\)). But if we consider the correct way, \(m\angle DGF = 180 - 71=109^{\circ}
eq142^{\circ}\).

Step4: Calculate \(m\angle AGF\)

\(m\angle AGC + m\angle FGC=38^{\circ}+147^{\circ}=185^{\circ}
eq128^{\circ}\)

Step5: Calculate \(\angle BGD\)

There is no information about \(\angle BGD\) calculation from the given \(m\angle AGC = 38^{\circ}\), \(m\angle CGD = 71^{\circ}\), and \(m\angle FGC = 147^{\circ}\) to confirm it's a right - angle.

Since there is not enough information to confirm any of the given statements based on the provided angle measures, no statements are true.

Answer:

None of the statements are true.